Many MAC protocols for mobile ad hoc networks using directional communication have been proposed recently. However, the common deficiency of them is that their assumed directional schemes on the physical layer are very ideal so that such schemes are hard-to-implement or even infeasible for more terminals. In this paper, a CSMA/CA based MAC protocol is designed for our previously proposed low complexity directional scheme. The feasibility of this scheme has been adequately considered with respect to dimension, power consumption and hardware complexity.